Quartz crystal resonator, unit having resonator, oscillator having unit, electronic apparatus having oscillator, and method for manufacturing electronic apparatus

ABSTRACT

A quartz crystal resonator has a quartz crystal tuning fork base and quartz crystal tuning fork tines connected to the quartz crystal tuning fork base. Each of the quartz crystal tuning fork tines has opposite main surfaces, a groove formed in at least one of the main surfaces, and an electrode disposed in the groove formed in at least one of the main surfaces so that a merit value M 1  of a fundamental mode of vibration of the quartz crystal tuning fork resonator is greater than a merit value M 2  of a second overtone mode of vibration thereof. The merit values M 1  and M 2  are defined by the ratios Q 1 /r 1  and Q 2 /r 2 , respectively, where Q 1  and Q 2  represent a quality factor of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator and r 1  and r 2  represent a capacitance ratio of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator. A piezoelectric constant e 12  of the the quartz crystal tuning fork resonator is within a range of 0.095 C/m 2  to 0.19 C/m 2  in the absolute value.

This application is a continuation-in-part of U.S. application Ser. No.10/378,719, filed Mar. 4, 2003, now abandoned.

FIELD OF THE INVENTION

The present invention relates to a quartz crystal resonator, a quartzcrystal unit having the quartz crystal resonator, a quartz crystaloscillator having the quartz crystal unit, an electronic apparatuscomprising at least a display portion and the quartz crystal oscillator,and a method for manufacturing the electronic apparatus.

BACKGROUND OF THE INVENTION

There are many electronic apparatuses comprising at least a displayportion and a quartz crystal oscillator. For example, cellular phones,wristwatches, facsimiles and pagers comprising a quartz crystaloscillator are well known. Recently, because of high stability forfrequency, miniaturization and the light weight nature of theseelectronic apparatuses, the need for an electronic apparatus comprisinga smaller quartz crystal oscillator with a high frequency stability hasarisen. For example, the quartz crystal oscillator with a quartz crystaltuning fork resonator, which is capable of vibrating in a flexural mode,is widely used as a time standard in an electronic apparatus such ascellular phones, wristwatches, facsimiles and pagers. Similar to this,the same need has also arisen for an electronic apparatus comprising alength-extensional mode quartz crystal resonator with a frequency of 1MHz to 10 MHz to decrease an electric current consumption of theelectronic apparatus.

Heretofore, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional miniaturized quartz crystal tuning fork resonator, capableof vibrating in a flexural mode, and having a high frequency stability,a small series resistance and a high quality factor. When miniaturized,the conventional quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, as shown in FIG. 12 (which has electrodeson the obverse faces 203, 207, reverse faces 204, 208 and the four sides205, 206, 209, 210 of each tuning fork tine, as also shown in FIG. 13—across-sectional view of tuning fork tines of FIG. 12), has a smallerelectromechanical transformation efficiency because the resonator shapeand the electrode construction provide a small electric field (i.e. Exbecomes small), as a result of which the resonator has a low frequencystability, a large series resistance a reduced quality factor. In FIG.12, a conventional tuning fork resonator 200 is shown with tines 201,202 and a base 230.

Moreover, for example, Japanese Patent Nos. P56-65517 and P2000-223992Aand International Patent No. WO 00/44092 were published and teachgrooves and electrodes constructed at tuning fork tines of a flexuralmode, tuning fork, quartz crystal resonator. However, they teach nothingabout a quartz crystal oscillator of the present invention having novelshape, novel electrode construction and figure of merit M for a quartzcrystal tuning fork resonator, capable of vibrating in a flexural modeand about a relationship of an amplification circuit and a feedbackcircuit which construct a quartz crystal oscillating circuit.

Additionally, for example, there has been a big problem in theconventional oscillator with the conventional quartz crystal tuning forkresonator, such that a fundamental mode vibration of the resonator jumpsto a second overtone mode vibration by shock or vibration.

Similarly, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional length-extensional mode quartz crystal resonator, capableof vibrating in a length-extensional mode, and having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor. Asan example of a length-extensional mode quartz crystal resonator of theprior art, the length-extensional mode resonator comprising avibrational portion, connecting portions and supporting portions, whichis formed from a Z plate perpendicular to z axis, is well known, andthis resonator is formed integrally by a chemical etching process. Also,electrodes are disposed opposite each other on sides of the vibrationalportion formed by the chemical etching process so that the electrodesdisposed opposite each other are of opposite electrical polarity.

Also, a cutting angle of the conventional length-extensional mode quartzcrystal resonator is generally within a range of ZYw(0° to +5°),according to an IEEE notation. In detail, the connecting portions areconnected opposite each other at both end portions of a width of thevibrational portion and at a central portion of the length directionthereof. Namely, the direction of the connecting portions constructedopposite each other corresponds to the direction of the electric field.

When an alternating current (AC) voltage is applied between theelectrodes, an electric field occurs alternately in the width direction,as a result, the resonator is capable of vibrating in the lengthdirection, but the electric field of between the electrodes becomes verysmall because quartz crystal is an anisotropic material and the sides ofthe vibrational portion have a complicated shape formed by the chemicaletching process. Namely, the resonator has small electromechanicaltransformation efficiency because the resonator's shape and theelectrode construction provide a small electric field, consequently, theresonator has a low frequency stability, a large series resistance and areduced quality factor when it has the frequency of 1 MHz to 10 MHz.

It is, therefore, a general object of the present invention to provideembodiments of an electronic apparatus and a quartz crystal oscillator,which constructs an electronic apparatus of the present invention,comprising a quartz crystal oscillating circuit with a flexural mode,quartz crystal tuning fork resonator, capable of vibrating in afundamental mode, and having a high frequency stability, a small seriesresistance and a high quality factor, or embodiments of a quartz crystaloscillator, which also constructs an electronic apparatus of the presentinvention, comprising a quartz crystal oscillating circuit with alength-extensional mode quartz crystal resonator having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor,which overcome or at least mitigate one or more of the above problems.

SUMMARY OF THE INVENTION

The present invention relates to an electronic apparatus comprising adisplay portion and a quartz crystal oscillator at least, and the quartzcrystal oscillator comprises a quartz crystal oscillating circuit havingan amplification circuit and a feedback circuit, and in particular,relates to a quartz crystal oscillator having a flexural mode, quartzcrystal tuning fork resonator capable of vibrating in a fundamental modeand having an output signal of a high frequency stability for thefundamental mode vibration of the resonator, and also to a quartzcrystal oscillator having a suppressed second overtone mode vibration ofthe flexural mode, quartz crystal tuning fork resonator, in addition,relates to a quartz crystal oscillator comprising a length-extensionalmode quartz crystal resonator. The quartz crystal oscillators are,therefore, available for the electronic apparatus requiring miniaturizedand low priced quartz crystal oscillators with high time accuracy andshock proof.

It is an object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with a miniature quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,and having a high frequency stability, a small series resistance R₁ anda high quality factor Q₁, whose nominal frequency for a fundamental modevibration is within a range of 10 kHz to 200 kHz.

It is an another object of the present invention to provide anelectronic apparatus comprising a quartz crystal oscillator with aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode, and having a high frequency stabilitywhich gives a high time accuracy.

It is a further object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with alength-extensional mode quartz crystal resonator.

According to one aspect of the present invention, there is provided anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least, and said electronic apparatus having one quartzcrystal oscillator, said one quartz crystal oscillator comprising: aquartz crystal oscillating circuit comprising; an amplification circuitcomprising an amplifier at least and a feedback circuit comprising aquartz crystal resonator and capacitors at least, said quartz crystalresonator being a quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, and said quartz crystal tuning forkresonator comprising: tuning fork tines each of which has a length, awidth and a thickness and the length greater than the width and thethickness; and a tuning fork base; said tuning fork tines and saidtuning fork base that are formed integrally; and electrodes disposedfacing each other on sides of said tuning fork tines so that theelectrodes disposed facing each other are of opposite electricalpolarity and said tuning fork tines are capable of vibrating in inversephase,

According to a second aspect of the present invention there is providedan electronic apparatus comprising a display portion and a quartzcrystal oscillator at least, and said electronic apparatus comprises atleast one quartz crystal oscillator comprising: an oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a length-extensional mode quartzcrystal resonator which is one of a contour mode quartz crystalresonator.

According to a third aspect of the present invention, there is provideda method for manufacturing an electronic apparatus comprising a displayportion and a quartz crystal oscillator at least, and said electronicapparatus comprising at least one quartz crystal oscillator, said atleast one oscillator comprising: a quartz crystal oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a quartz crystal resonator andcapacitors at least, said quartz crystal resonator being a quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,said quartz crystal tuning fork resonator comprising the steps of:forming integrally tuning fork tines each of which has a length, a widthand a thickness and the length greater than the width and the thicknessand a tuning fork base; disposing electrodes facing each other on sidesof said tuning fork tines so that the electrodes disposed facing eachother are of opposite electrical polarity and said tuning fork tinesvibrate an in inverse phase; and adjusting resonance frequency of saidquartz crystal tuning fork resonator after mounting it at a mountingportion by conductive adhesives or solder so that a frequency deviationis within a range of −100 PPM to +100 PPM.

According to a fourth aspect of the present invention, there areprovided a quartz crystal resonator, a quartz crystal unit and a quartzcrystal oscillator, each of which has a piezoelectric constant e₁₂ thatis within a range of 0.095 C/m² to 0.19 C/m².

Preferably, said tuning fork resonator is constructed so that figure ofmerit M₁ of a fundamental mode vibration is larger than figure of meritM₂ of a second overtone mode vibration.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an amplification rate α₁ ofthe fundamental mode vibration and an amplification rate α₂ of thesecond overtone mode vibration of said amplification circuit is largerthan that of a feedback rate β₂ of the second overtone mode vibrationand a feedback rate β₁ of the fundamental mode vibration of saidfeedback circuit, and a product of the amplification rate α₁ and thefeedback rate β₁ of the fundamental mode vibration is larger than 1.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an absolute value ofnegative resistance, |−RL₁| of the fundamental mode vibration of saidamplification circuit and series resistance R₁ of the fundamental modevibration is larger than that of an absolute value of negativeresistance, |−RL₂| of the second overtone mode vibration of saidamplification circuit and series resistance R₂ of the second overtonemode vibration.

Preferably, the length-extensional mode quartz crystal resonatorcomprises a vibrational portion, connecting portions and supportingportions, which are formed integrally by a particle method.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus;

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention;

FIG. 3 shows a diagram of the feedback circuit of FIG. 2;

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the first embodiment of thepresent invention;

FIG. 5 shows a D–D′ cross-sectional view of the tuning fork base of FIG.4, and illustrating electrode construction;

FIG. 6 shows a plan view of a quartz crystal tuning fork resonator ofFIG. 4;

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the second embodiment of the present invention;

FIG. 8 a and FIG. 8 b show a top view and a side view of alength-extensional mode quartz crystal resonator constructing a quartzcrystal oscillator, which constructs an electronic apparatus of thethird embodiment of the present invention;

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention;

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention;

FIG. 11 shows a step diagram of a method for manufacturing a quartzcrystal unit constructing a quartz crystal oscillator, which constructsan electronic apparatus of the present invention;

FIG. 12 is a general view of the conventional flexural mode, quartzcrystal tuning fork resonator constructing a quartz crystal oscillatorof the prior art, which constructs the conventional electronicapparatus; and

FIG. 13 is a cross-sectional view of the tuning fork tines of FIG. 12,and illustrating electrode construction.

DETAILED DESCRIPTION

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus. As is shown in FIG. 1, the apparatus generally comprises amodem, a phonetic circuit, a timepiece circuit, a printing portion, ataking portion, an operation portion and a display portion. In thisprinciple, perception and scanning of reflection light of lightprojected on manuscript in the taking portion are performed byCCD(Charge Coupled Device), in addition, light and shade of thereflection light are transformed into a digital signal, and the signalis modulated by the modem and is sent to a phone line(Communicationline). Also, in a receiving side, a received signal is demodulated bythe modem and is printed on a paper in the print portion bysynchronizing the received signal with a signal of a sending side.

As shown in FIG. 1, a quartz crystal resonator is used as a CPU clock ofthe control portion and the printing portion, as a clock of the phoneticcircuit and the modem, and as a time standard of the timepiece. Namely,the resonator constructs a quartz crystal oscillator and an outputsignal of the oscillator is used. For example, it is used as a signal todisplay time at the display portion. In this case, a quartz crystaltuning fork resonator, capable of vibrating in a flexural mode is used,and e.g. as the CPU clock, a contour mode quartz crystal resonator suchas a length-extensional mode quartz crystal resonator or a thicknessshear mode quartz crystal resonator is used. In order to get thefacsimile apparatus of this embodiment which operates normally, anaccuracy output signal of the oscillator is required for the facsimileapparatus, which is one of the electronic apparatus of the presentinvention. Also, a digital display and an analogue display are includedin the display of the present invention.

In this embodiment, though the facsimile apparatus is shown as anexample of an electronic apparatus, the present invention is not limitedto this, namely, the present invention includes all electronicapparatus, each of which comprises a quartz crystal oscillator and adisplay portion at least, for example, cellar phones, telephones, a TVset, cameras, a video set, video cameras, pagers, personal computers,printers, CD players, MD players, electronic musical instruments, carnavigators, car electronics, timepieces, IC cards and so forth.

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention. The quartz crystaloscillating circuit 1 comprises an amplifier (CMOS Inverter) 2, afeedback resistor 4, a drain resistor 7, capacitors 5, 6 and a flexuralmode, quartz crystal tuning fork resonator 3. Namely, the oscillatingcircuit 1 comprises an amplification circuit 8 having the amplifier 2and the feedback resistor 4, and a feedback circuit 9 having the drainresistor 7, the capacitors 5, 6 and the quartz crystal tuning forkresonator 3. In addition, an output signal of the oscillating circuit 1comprising the quartz crystal tuning fork resonator 3, capable ofvibrating in a fundamental mode, is outputted through a buffer circuit(not shown in FIG. 2).

In detail, an oscillation frequency of the fundamental mode vibration isoutputted through a buffer circuit as an output signal. According to thepresent invention, a nominal frequency of the fundamental mode vibrationof the resonator is within a range of 10 kHz to 200 kHz. Especially,32.768 kHz is an important frequency. In general, the output signal hasan oscillation frequency which is within a range of −100 PPM to +100 PPMto the nominal frequency, e.g. 32.768 kHz. In more detail, the quartzcrystal oscillator in this embodiment comprises a quartz crystaloscillating circuit and a buffer circuit, namely, the quartz crystaloscillating circuit comprises an amplification circuit and a feedbackcircuit, and the amplification circuit comprises an amplifier and afeedback resistor, and the feedback circuit comprises a flexural mode,quartz crystal tuning fork resonator, a drain resistor and capacitors.Also, flexural mode, quartz crystal tuning fork resonators which areused in a quartz crystal oscillator will be described in FIG. 4–FIG. 7in detail. Instead of the flexural mode, quartz crystal tuning forkresonator, a contour mode resonator such as a length-extensional modequartz crystal resonator, a width-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator or a thickness shearmode quartz crystal resonator may be used.

FIG. 3 shows a diagram of the feedback circuit of FIG. 2. Now, whenangular frequency ω_(i) of the flexural mode, quartz crystal tuning forkresonator 3, capable of vibrating in a flexural mode, a resistance R_(d)of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5,6, crystal impedance R_(ei) of the quartz crystal resonator 3, an inputvoltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) isdefined by β_(i)=|V₂|_(i)/|V₁|_(i), where i shows vibration order, forexample, when i=1 and 2, they are for a fundamental mode vibration and asecond overtone mode vibration.

In addition, load capacitance C_(L) is given by C_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) and R_(d)>>R_(ei), thefeedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²), where k isexpressed by a function of ω_(i), R_(d) and R_(ei). Also, R_(ei), isapproximately equal to series resistance R_(i).

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of resonancefrequency for a fundamental mode vibration and an overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when C_(L) has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

As it is also one object of the present invention to provide a quartzcrystal oscillator having a flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having a highfrequency stability (high time accuracy) of an output signal, and havingreduced electric current consumption, in this embodiment, loadcapacitance C_(L) is less than 25 pF to reduce electric currentconsumption. To get much reduced electric current consumption, C_(L) ispreferably less than 15 pF because electric current consumption isproportional to C_(L).

In addition, in order to suppress a second overtone mode vibration andto obtain a quartz crystal oscillator having an output signal of anoscillation frequency of a fundamental mode vibration, the quartzcrystal oscillator in this embodiment is constructed so that itsatisfies a relationship of α₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are,respectively, an amplification rate of the fundamental mode vibrationand the second overtone mode vibration of an amplification circuit, andβ₁ and β₂ are, respectively, a feedback rate of the fundamental modevibration and the second overtone mode vibration of a feedback circuit.

In other words, the quartz crystal oscillator is constructed so that aratio of the amplification rate α₁ of the fundamental mode vibration andthe amplification rate α₂ of the second overtone mode vibration of theamplification circuit is larger than that of the feedback rate β₂ of thesecond overtone mode vibration and the feedback rate β₁ of thefundamental mode vibration of the feedback circuit, and also a productof the amplification rate α₁ and the feedback rate β₁ of the fundamentalmode vibration is larger than 1. A description of the high frequencystability will be performed later.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode vibration and wheni=2, negative resistance −RL₂ is for a second overtone mode vibration.In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult of which an output signal of a frequency of the fundamental modevibration can be provided because an oscillation of the fundamental modegenerates easily in the oscillating circuit.

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator 10 which is one of a contour mode resonator, constructinga quartz crystal oscillator, which constructs an electronic apparatus ofthe first embodiment of the present invention and its coordinate systemo-xyz. A cut angle θ which has a typical value of 0° to 10° is rotatedfrom a Z-plate perpendicular to the z axis about the x axis. Theresonator 10 comprises two tuning fork tines (vibrating tines) 20 and 26and a tuning fork base (a base) 40. The tines 20 and 26 have grooves 21and 27 respectively, with the grooves 21 and 27 extending into the base40. Also, the base 40 has the additional grooves 32 and 36. In addition,the tines 20 and 26 vibrate in a flexural mode of a fundamental mode andan inverse phase.

FIG. 5 shows a D–D′ cross-sectional view of the tuning fork base 40 ofthe quartz crystal resonator 10 in FIG. 4. In FIG. 5, the shape of theelectrode construction within the base 40 for the quartz crystalresonator of FIG. 4 is described in detail. The section of the base 40which couples to the tine 20 has the grooves 21 and 22 cut into theobverse and reverse faces of the base 40. Also, the section of the base40 which couples to the tine 26 has the grooves 27 and 28 cut into theobverse and reverse faces of the base 40. In addition to these grooves,the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27,and also, the base 40 has the grooves 33 and 37 cut between the grooves22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24both of the same electrical polarity, the grooves 32 and 33 have thesecond electrodes 34 and 35 both of the same electrical polarity, thegrooves 36 and 37 have the third electrodes 38 and 39 both of the sameelectrical polarity, the grooves 27 and 28 have the fourth electrodes 29and 30 both of same electrical polarity and the sides of the base 40have the fifth and sixth electrodes 25 and 31, each of oppositeelectrical polarity. In more detail, the fifth, fourth, and secondelectrodes 25, 29, 30, 34 and 35 have the same electrical polarity,while the first, sixth and third electrodes 23, 24, 31, 38 and 39 havethe opposite electrical polarity to the others. Two electrode terminalsE–E′ are constructed. That is, the electrodes disposed inside thegrooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

In addition, the resonator has a thickness t of the tines or the tinesand the base, and a groove thickness t₁. It is needless to say that theelectrodes are disposed inside the grooves and on the sides of thetines. In this embodiment, the first electrodes 23 and 24 are disposedat the tine and the base, and also, the fourth electrodes 29 and 30 aredisposed at the tine and the base. In addition, the electrodes aredisposed on the sides of the tines opposite each other to the electrodesdisposed inside the grooves. Namely, the electrodes are disposedopposite each other inside the grooves and on the sides of the tines sothat the electrodes disposed opposite each other are of oppositeelectrical polarity. Additionally, electrodes are disposed facing eachother on the sides of the tines so that the electrodes disposed facingeach other are of opposite electrical polarity, and the tines arecapable of vibrating in inverse phase. In more detail, a first tuningfork tine and a second tuning fork tine, and a tuning fork base areformed integrally, an electrode is disposed on both sides of the firsttine and the second tine so that the electrodes disposed (facing eachother) on inner sides of the first and second tines are of oppositeelectrical polarity.

When a direct voltage is applied between the electrode terminals E–E′ (Eterminal: plus, E′ terminal: minus), an electric field E_(x) occurs inthe arrow direction as shown in FIG. 5. As the electric field E_(x)occurs perpendicular to the electrodes disposed on the base, theelectric field E_(x) has a very large value and a large distortionoccurs at the base, so that the quartz crystal tuning fork resonator isobtained with a small series resistance R₁ and a high quality factor Q₁,even if it is miniaturized.

FIG. 6 shows a plan view of the resonator 10 of FIG. 4. In FIG. 6, theconstruction and the dimension of grooves 21, 27, 32 and 36 aredescribed in detail. The groove 21 is constructed to include a portionof the central line 41 of the tine 20, and the groove 27 is similarlyconstructed to include a portion of the central line 42 of the tine 26.The width W₂ of the grooves 21 and 27 (groove width W₂) which include aportion of the central lines 41 and 42 respectively, is preferablebecause moment of inertia of the tines 20 and 26 becomes large and thetines can vibrate in a flexural mode easily. As a result, the quartzcrystal tuning fork resonator capable of vibrating in a fundamental modecan be obtained with a small series resistance R₁ and a high qualityfactor Q₁.

In more detail, when part widths W₁, W₃ and a groove width W₂ are taken,the tine width W of the tines 20 and 26 has a relationship ofW=W₁+W₂+W₃, and the part widths W₁,W₃ are constructed so that W₁≧W₃ orW₁<W₃. In addition, the groove width W₂ is constructed so that W₂≧W₁,W₃. In this embodiment, also, the grooves are constructed at the tinesso that a ratio (W₂/W) of the groove width W₂ and the tine width W islarger than 0.35 and less than 1, and a ratio (t₁/t) of the groovethickness t₁ and the thickness t of the tines (tine thickness t) is lessthan 0.79, to obtain very large moment of inertia of the tines. That is,the flexural mode, quartz crystal tuning fork resonator, capable ofvibrating in the fundamental mode, and having a good frequency stabilitycan be provided with a small series resistance R₁, a high quality factorQ₁ and a small capacitance ratio r₁ because electromechanicaltransformation efficiency of the resonator becomes large markedly.

Likewise, a length l₁ of the grooves 21, 27 provided at the tines 20, 26extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, a groovelength and a length of the tines are given by (l₁–l₃) and (l–l₂),respectively, and a ratio of (l₁–l₃) and (l–l₂) is within a range of 0.4to 0.8 to get a flexural mode tuning fork resonator with seriesresistance R₁ of a fundamental mode vibration smaller than seriesresistance R₂ of a second overtone mode vibration. Also, a length l₂ ofthe base is less than 0.5 mm.

Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. Simultaneously, to get aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode with suppression of the second overtonemode vibration which is an unwanted mode vibration, there is a closerelationship between the groove length l₁ and the total length l.Namely, a ratio (l₁/l) of the groove length l₁ and the total length l iswithin a range of 0.2 to 0.78 because the quantity of charges whichgenerate within the grooves and on the sides of the tines or the tinesand the base can be controlled by the ratio, as a result, the secondovertone mode vibration which is an unwanted mode vibration, can besuppressed, and simultaneously, a frequency stability of the fundamentalmode vibration gets high. Therefore, the flexural mode, quartz crystaltuning fork resonator, capable of vibrating easily in a fundamental modeand having high frequency stability can be provided. Also, the totallength l is less than 2.18 mm, preferably, within a range of 1.2 mm to 2mm, and groove length l₁ is less than 1.29 mm, preferably, within arange of 0.35 mm to 1.15 mm, to get a smaller-sized tuning forkresonator which vibrates in a flexural mode and a fundamental mode.

In more detail, series resistance R₁ of the fundamental mode vibrationbecomes smaller than series resistance R₂ of the second overtone modevibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartzcrystal oscillator comprising an amplifier (CMOS inverter), capacitors,resistors and a quartz crystal unit with the quartz crystal tuning forkresonator of this embodiment can be obtained, which is capable ofvibrating in the fundamental mode easily. In addition, in thisembodiment the grooves 21 and 27 of the tines 20 and 26 extend into thebase 40 in series, but embodiment of the present invention includes aplurality of grooves divided into the length direction of the tines. Inaddition, the grooves may be constructed only at the tines (l₃=0).

In this embodiment, the groove length l₁ corresponds to electrode lengthdisposed inside the grooves, though the electrode is not shown in FIG.6, but, when the electrode length is less than the groove length, thelength l₁ is of the electrode length. Namely, the ratio (l₁/l) in thiscase is expressed by a ratio of electrode length l₁ of the grooves andthe total length l. In order to achieve the above-mentioned object, itmay be satisfied with at least one groove with the ratio constructed atthe obverse and reverse faces of each tine. As a result, the flexuralmode, quartz crystal tuning fork resonator, capable of vibrating veryeasily in the fundamental mode and having the high frequency stabilitycan be realized. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

In addition, a space of between the tines is given by W₄, and in thisembodiment, the space W₄ and the groove width W₂ are constructed so thatW₄≧W₂, and more, the space W₄ is within a range of 0.05 mm to 0.35 mmand the groove width W₂ is within a range of 0.03 mm to 0.12 mm becauseit is easy to form a tuning fork shape and grooves of the tuning forktines separately by a photo-lithographic process and an etching process,consequently, a frequency stability for a fundamental mode vibrationgets higher than that for a second overtone mode vibration. In thisembodiment, a quartz wafer with the thickness t of 0.05 mm to 0.15 mm isused. In order to get a smaller-sized quartz crystal tuning forkresonator, capable of vibrating in a flexural mode, it is necessary thatgroove width W₂ is less than 0.7 mm and tine width W is less than 0.18mm, and preferably, the W is larger than 0.05 mm and less than 0.1 mm.Also, a groove thickness t₁ is within a range of 0.01 mm to 0.085 mmapproximately, and part widths W₁, W₃ are less than 0.021 mm,respectively, preferably, less than 0.015 mm. In addition, a grooveprovided on at least one of an obverse face and a reverse face of tuningfork tines of the present invention may be a through hole, namely, agroove thickness t₁=0.

In more detail, to obtain a flexural mode, quartz crystal tuning forkresonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) plays an important role. Namely, the figure of merit M_(i) thatexpresses inductive characteristics, electromechanical transformationefficiency and a quality factor of a flexural mode, quartz crystaltuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a qualityfactor Q_(i) and capacitance ratio r_(i), namely, M_(i) is given byM_(i)=Q_(i)/r_(i), where i shows vibration order of the resonator, andfor example, when i=1 and 2, figures of merit M₁ and M₂ are a value fora fundamental mode vibration and a second overtone mode vibration of theflexural mode, quartz crystal tuning fork resonator, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the figure of merit M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal tuning fork resonator becomes because the resonancefrequency f_(r) of the resonator is almost never dependent on the shuntcapacitance. Namely, the quartz crystal tuning fork resonator can beprovided with a high time accuracy.

In detail, the flexural mode, quartz crystal tuning fork resonator canbe obtained with figure of merit M₁ of the fundamental mode vibrationlarger than figure of merit M₂ of the second overtone mode vibration bythe above-described tuning fork shape, grooves and dimensions. That isto say, a relationship of M₁>M₂ is obtained. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, the resonator has a value of M₁>65 andM₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator whichvibrates in the fundamental mode can be provided with high inductivecharacteristics, good electromechanical transformation efficiency (smallcapacitance ratio r₁ and small series resistance R₁) and a high qualityfactor. As a result, a frequency stability of the fundamental modevibration becomes higher than that of the second overtone modevibration, and simultaneously, the second overtone mode vibration can besuppressed because capacitance ratio r₂ and series resistance R₂ of thesecond overtone mode vibration become larger than capacitance ratio r₁and series resistance R₁ of the fundamental mode vibration,respectively. In particular, r₂ has a value larger than 1500 in thisembodiment.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thehigh frequency stability. Consequently, a quartz crystal oscillatorcomprising the flexural mode, quartz crystal tuning fork resonator ofthis embodiment outputs an oscillation frequency of the fundamental modevibration as an output signal, and the frequency of the output signalhas a very high stability, namely, excellent time accuracy. In otherwords, the quartz crystal oscillator of this embodiment has a remarkableeffect such that a frequency change by ageing becomes extremely small.Also, an oscillation frequency of the resonator of this embodiment isadjusted so that a frequency deviation is within a range of −100 PPM to+100 PPM to a nominal frequency, e.g. 32.768 kHz, after mounting it at amounting portion of a case or a lid by conductive adhesives or solder.

In addition, the groove thickness t₁ of the present invention is thethinnest thickness of the grooves because quartz crystal is ananisotropic material and the groove thickness t₁ has a distribution whenit is formed by a chemical etching method. In detail, a groove shape ofthe sectional view of tuning fork tines in FIG. 5 has a rectangularshape, but the groove shape has an about U shape actually. In theabove-described embodiments, though the grooves are constructed at thetines, this invention is not limited to this, namely, a relationship ofthe figures of merit M₁ and M₂ can be applied to the conventionalflexural mode, quartz crystal tuning fork resonator and a relationshipof a quartz crystal oscillating circuit comprising an amplificationcircuit and a feedback circuit can be also applied to the conventionalflexural mode, quartz crystal tuning fork resonator to suppress a secondovertone mode vibration and to get a high frequency stability for afundamental mode vibration of the tuning fork resonator.

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator 45 which is one of a contour mode quartz crystal resonator,constructing a quartz crystal oscillator, which constructs an electronicapparatus of the second embodiment of the present invention. Theresonator 45 comprises tuning fork tines 46, 47 and a tuning fork base48. The tines 46, 47 and the base 48 are formed integrally by a chemicaletching process. In this embodiment, the base 48 has cut portions 53 and54. Also, a groove 49 is constructed to include a portion of the centralline 51 of the tine 46, and a groove 50 is similarly constructed toinclude a portion of the central line 52 of the tine 47. In thisembodiment, the grooves 49 and 50 are constructed at a part of the tines46 and 47, and have groove width W₂ and groove length l₁. In moredetail, a groove area S (=W₂×l₁) has a value of 0.025 mm² to 0.12 mm²because it is very easy to form the grooves by a chemical etchingprocess and the quartz crystal tuning fork resonator can be providedwith good electromechanical transformation efficiency by the formationof the grooves.

Namely, the quartz crystal tuning fork resonator, capable of vibratingin a fundamental mode and having a high frequency stability can beprovided with a small series resistance R₁ and a high quality factor Q₁.Therefore, a quartz crystal oscillator having the high frequencystability can be realized with an output signal of a frequency of thefundamental mode vibration. In this embodiment, though electrodes arenot shown in FIG. 7, the electrodes are disposed inside the grooves 49,50 and on sides of the tines 46 and 47, similar to the resonator of FIG.4. In detail, the electrodes are disposed opposite each other inside thegrooves and on the sides of the tines so that the electrodes disposedopposite each other are of opposite electrical polarity. In more detail,a groove is provided on both of an obverse face and a reverse face oftuning fork tines having a first tuning fork tine and a second tuningfork tine, and also, a first electrode is disposed inside the groove anda second electrode is disposed on both sides of the tuning fork tines.In addition, a quartz crystal tuning fork resonator has two electrodeterminals, the one of the electrode terminals comprises a firstelectrode disposed inside a groove provided on both of the obverse faceand the reverse face of the first tuning fork tine and a secondelectrode disposed on the both sides of the second tuning fork tine,such that the first and second electrodes are connected, and the otherof the electrode terminals comprises a second electrode disposed on theboth sides of the first tuning fork tine and a first electrode disposedinside a groove provided on both of the obverse face and the reverseface of the second tuning fork tine, such that the second and firstelectrodes are connected. In this embodiment, a groove is provided onboth of an obverse face and a reverse face of tuning fork tines, but thepresent invention in not limited to this, for example, a groove may beprovided on at least one of an obverse face and a reverse face of tuningfork tines.

In addition, the base 48 has cut portions 53 and 54, and the cut base 48has a dimension of width W₅ (tines side) and width W₆ (opposite side tothe tines side). When the base 48 is mounted at a mounting portion(e.g.on two lead wires for a package of a tubular type) of a case or a lid ofa surface mounting type or a tubular type by solder or conductiveadhesives, it is necessary to satisfy W₆≧W₅ to decrease energy losses byvibration. The cut portions 53 and 54 are very effective to decrease theenergy losses. Therefore, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating in the fundamental mode and having thehigh frequency stability (high time accuracy) can be provided with asmall series resistance R₁ and a high quality factor Q₁. Also, the widthdimensions W=W₁+W₂+W₃ and W₄, and the length dimensions l₁, l₂ and l areas already described in relation to FIG. 6. In addition, a shape of thetuning fork base according to the present invention is not limited tothat of this embodiment, for example, a tuning fork base may have aframe portion protruding from the tuning fork base, and the frameportion is mounted at a mounting portion of a case or a lid of apackage.

FIG. 8 a and FIG. 8 b are a top view and a side view for alength-extensional mode quartz crystal resonator which is one of acontour mode resonator, constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the third embodiment of thepresent invention. The resonator 62 comprises a vibrational portion 63,connecting portions 66, 69 and supporting portions 67, 80 includingrespective mounting portions 68, 81. In addition, the supportingportions 67 and 80 have respective holes 67 a and 80 a. Also, electrodes64 and 65 are disposed opposite each other on upper and lower faces ofthe vibrational portion 63, and the electrodes have opposite electricalpolarities. Namely, a pair of electrodes is disposed on the vibrationalportion. In this case, a fundamental mode vibration can be excitedeasily.

In addition, the electrode 64 extends to the mounting portion 81 throughthe one connecting portion 69 and the electrode 65 extends to themounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. But, the electrodes may be constructed in the same direction. Theresonator in this embodiment is mounted on fixing portions of a case ora lid at the mounting portions 68 and 81 by conductive adhesives orsolder.

Here, a cutting angle of the length-extensional mode quartz crystalresonator is shown. First, a quartz crystal plate perpendicular to xaxis, so called, X plate quartz crystal is taken. Length L₀, width W₀and thickness T₀ which are each dimension of the X plate quartz crystalcorrespond to the respective directions of y, z and x axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x)of −30° to +30° about the x axis, and second, rotated with an angleθ_(y) of −40° to +40° about y′ axis which is the new axis of the y axis.In this case, the new axis of the x axis changes to x′ axis and the newaxis of the z axis changes to z″ axis because the z axis is rotatedtwice about two axes. The length-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the resonator of the present invention can be expressed byXYtl(−30° to +30°)/(−40° to +40°). By choosing a cutting angle of theresonator, a turn over temperature point T_(p) can be taken at anarbitrary temperature. In this embodiment, length L₀, width W₀ andthickness T₀ correspond to y′, z″ and x′ axes, respectively. But, whenthe X plate is rotated once about the x axis, the z″ axis corresponds tothe z′ axis. In addition, the vibrational portion 63 has a dimension oflength L₀ greater than width W₀ and thickness T₀ smaller than the widthW₀. Namely, a coupling between length-extensional mode andwidth-extensional mode gets so small as it can be ignored, as a resultof which, the quartz crystal resonator can vibrate in a singlelength-extensional mode.

In more detail, resonance frequency of the length-extensional moderesonator is inversely proportional to length L₀, and it is almostindependent on such an other dimension as width W₀, thickness T₀,connecting portions and supporting potions. Also, in order to obtain alength-extensional mode quartz crystal resonator capable of vibrating ina fundamental mode with a frequency of 1 MHz to 10 MHz, the length L₀ iswithin a range of about 0.26 mm to about 2.7 mm. In addition, when alength-extensional mode resonator vibrates in an overtone mode, an oddnumber (n) pair of electrodes are disposed on a vibrational portion ofthe resonator, where n has a value of 1,3,5, . . . In this case, thelength L₀ is a range of about (0.26 to 2.7)×n mm. Thus, the miniaturelength-extensional mode resonator can be provided with the frequency of1 MHz to 10 MHz.

Next, a value of a piezoelectric constant e₁₂ (=e′₁₂) is described,which is of great importance and necessary to excite a flexural mode,quartz crystal resonator and a length-extensional mode quartz crystalresonator of the present invention. The larger a value of thepiezoelectric constant e₁₂ becomes, the higher electromechanicaltransformation efficiency becomes. The piezoelectric constant e₁₂ of thepresent invention can be calculated using the piezoelectric constantse₁₁=0.171 C/m² and e₁₄=−0.0406 C/m² of quartz crystal. As a result, thepiezoelectric constant e₁₂ of the present invention is within a range of0.095 C/m² to 0.19 C/m² approximately in an absolute value. It is,therefore, easily understood that this value is enough large to obtain aflexural mode, quartz crystal tuning fork resonator and alength-extensional mode quartz crystal resonator with a small seriesresistance R₁ and a high quality factor Q. Especially, in order toobtain a flexural mode, quartz crystal tuning fork resonator with asmaller series resistance R₁, the e₁₂ is within a range of 0.12 C/m² to0.19 C/m² in the absolute value, and also, a groove and electrodes areprovided on at least one of an obverse face and a reverse face of tuningfork tines so that when each tuning fork tine is divided into twoportions (an inner portion located at a fork side and an outer portionlocated opposite to the fork side) versus a central line portionthereof, a value of e₁₂ of each portion of each tuning fork tine has anopposite sign each other. Namely, when the one of the two portions hase₁₂ of a plus sign, the other of the two portions has e₁₂ of a minussign. In more detail, a groove and electrodes are provided at tuningfork tines so that a sign of e₁₂ of inner portions of each tuning forktine is opposite to the sign of e₁₂ of outer portions of each tuningfork tine.

When an alternating current voltage is applied between the electrodes 64and 65 shown in FIG. 8 b, an electric field E_(x) occurs alternately inthe thickness direction, as shown by the arrow direction of the solidand broken lines in FIG. 8 b. Consequently, the vibrational portion 63is capable of extending and contracting in the length direction.

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention. The quartzcrystal unit 170 comprises a contour mode quartz crystal resonator 70 ora thickness shear mode quartz crystal resonator 70, a case 71 and a lid72. In more detail, the resonator 70 is mounted at a mounting portion 74of the case 71 by conductive adhesives 76 or solder. Also, the case 71and the lid 72 are connected through a connecting member 73. Forexample, the contour mode resonator 70 in this embodiment is the sameresonator as one of the flexural mode, quartz crystal tuning forkresonators 10 and 45 described in detail in FIG. 4–FIG. 7. Also, in thisembodiment, circuit elements are connected at outside of the quartzcrystal unit to get a quartz crystal oscillator. Namely, only the quartzcrystal tuning fork resonator is housed in the unit and also, it ishoused in the unit in vacuum. In this embodiment, the quartz crystalunit of a surface mounting type is shown, but the quartz crystal tuningfork resonator may be housed in a tubular type, namely a quartz crystalunit of the tubular type. Also, instead of the flexural mode, quartzcrystal tuning fork resonator and the thickness shear mode quartzcrystal resonator, one of a length-extensional mode quartz crystalresonator, a width-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator which are a contour mode resonator,respectively, or a SAW (Surface Acoustic Wave) resonator may be housedin the unit. In addition, the present invention is not limited to thequartz crystal unit having the contour mode quartz crystal resonator orthe thickness shear mode quartz crystal resonator in this embodiment,for example, the present invention also includes a quartz crystal unithaving a piezoelectric filter, e.g. a SAW piezoelectric filter or apiezoelectric sensor, e.g. an angular velocity piezoelectric sensor.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 10.

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention. The quartz crystal oscillator 190 comprises a quartzcrystal oscillating circuit, a case 91 and a lid 92. In this embodiment,circuit elements constructing the oscillating circuit are housed in aquartz crystal unit comprising a contour mode quartz crystal resonator90 or a thickness shear mode quartz crystal resonator 90, the case 91and the lid 92. Also, the oscillating circuit of this embodimentcomprises an amplifier 98 including a feedback resistor, the resonator90, capacitors (not shown here) and a drain resistor (not shown here),and a CMOS inverter is used as the amplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. For example, the contour moderesonator 90 of this embodiment is the same as one of the flexural mode,quartz crystal tuning fork resonators 10 and 45 described in detail inFIG. 4–FIG. 7. Also, instead of the flexural mode, quartz crystal tuningfork resonator and the thickness shear mode quartz crystal resonator,one of a length-extensional mode quartz crystal resonator, awidth-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator which are a contour mode resonator, respectively, or aSAW (Surface Acoustic Wave) resonator may be housed in the unit.

Likewise, in this embodiment, a piece of flexural mode, quartz crystaltuning fork resonator is housed in the unit, but the present inventionalso includes a quartz crystal unit having a plurality of flexural mode,quartz crystal tuning fork resonators, and at least two of the pluralityof resonators are connected electrically in parallel. In addition, theat least two resonators may be an individual resonator or may beindividual resonators that are formed integrally at each tuning basethrough a connecting portion.

Next, a method for manufacturing a quartz crystal oscillator, whichconstructs an electronic apparatus of the present invention, isdescribed in detail, according to the manufacturing steps.

FIG. 11 shows an embodiment of a method for manufacturing a quartzcrystal oscillator, which constructs an electronic apparatus of thepresent invention and a step diagram embodying the present invention.The signs of S-1 to S-12 are the step numbers. First, S-1 shows across-sectional view of a quartz crystal wafer 140. Next, in S-2 metalfilm 141, for example, chromium and gold on the chromium are,respectively, disposed on upper and lower faces of the quartz crystalwafer 140 by an evaporation method or a spattering method. In addition,resist 142 is spread on said metal film 141 in S-3, and after the metalfilm 141 and the resist 142 were removed except those of tuning forkshape by a photo-lithographic process and an etching process, the tuningfork shape with tuning fork tines 143, 144 and a tuning fork base 145,as be shown in S-4, is integrally formed by a chemical etching process.When the tuning fork shape is formed, cut portions may be formed at thetuning fork base. In FIG. 11, the formation of a piece of tuning forkshape is shown, but, a number of tuning fork shapes are actually formedin a piece of quartz crystal wafer.

Similar to the steps of S-2 and S-3, metal film and resist are spreadagain on the tuning fork shape of S-4 and grooves 146, 147, 148 and 149each of which has two step difference portions along the lengthdirection of the tuning fork tines, are formed at the tuning fork tines143, 144 by the photo-lithographic process and the etching process, andthe shape of S-5 is obtained after all of the resist and the metal filmwere removed. In addition, metal film and resist are spread again on theshape of S-5 and electrodes which are of opposite electrical polarity,are disposed on sides of the tines and inside the grooves thereof, as beshown in S-6.

Namely, electrodes 150, 153 disposed on the sides of the tuning forktine 143 and electrodes 155, 156 disposed inside the grooves 148, 149 ofthe tuning fork tine 144 have the same electrical polarity. Similarly,electrodes 151, 152 disposed inside the grooves 146, 147 of the tuningfork tine 143 and electrodes 154, 157 disposed on the sides of thetuning fork tine 144 have the same electrical polarity. Two electrodeterminals are, therefore, constructed. In more detail, when analternating current (AC) voltage is applied between the terminals, thetuning fork tines vibrate in a flexural mode of an inverse phase becausesaid electrodes disposed on step difference portions of the grooves andthe electrodes disposed opposite to the said electrodes have oppositeelectrical polarity. In the step of S-6, a piece of quartz crystaltuning fork resonator, capable of vibrating in a flexural mode is shownin the quartz crystal wafer, but a number of quartz crystal tuning forkresonators are actually formed in the wafer.

In addition, a resonance (oscillation) frequency for said resonators isadjusted by a separate step of at least twice and the first adjustmentof resonance frequency for said resonators is performed in the quartzcrystal wafer by a laser method or an evaporation method or an ionetching method so that a frequency deviation of said resonators iswithin a range of −9000 PPM to +5000 PPM (Parts Per Million) to anominal frequency of 10 kHz to 200 kHz, e.g. 32.768 kHz. The adjustmentof frequency by the laser or ion etching method is performed by trimmingmass disposed on tuning fork tines and the adjustment of frequency bythe evaporation method is performed by adding mass on tuning fork tines.Namely, those methods can change the resonance (oscillation) frequencyof said resonators. Also, the resonators formed in the quartz crystalwafer are inspected therein and when there is a failure resonator, it isremoved from the wafer or something is marked on it or it is rememberedby a computer.

In this embodiment, the tuning fork shape is formed from the step of S-3and after that, the grooves are formed at the tuning fork tines, namely,the tuning fork tines are formed before the grooves are formed, but thisinvention is not limited to said embodiment, for example, the groovesare first formed from the step of S-3 and after that, the tuning forkshape may be formed, namely, the grooves are formed before the tuningfork tines are formed. Also, the tuning fork shape and the grooves maybe formed simultaneously, namely, the tuning fork tines and the groovesare formed simultaneously.

There are two methods of A and B in the following step, as be shown byarrow signs. For the step of A, the tuning fork base 145 of the formedflexural mode, quartz crystal tuning fork resonator 160 is first mountedon mounting portion 159 of a case 158 by conductive adhesives 161 orsolder, as be shown in S-7. Next, the second adjustment of resonance(oscillation) frequency for the resonator 160 is performed by laser 162or evaporation or ion etching method in S-8 so that a frequencydeviation is within a range of −100 PPM to +100 PPM to the nominalfrequency of 10 kHz to 200 kHz, e.g. 32.768 kHz. Finally, the case 158and a lid 163 are connected via glass 164 with the low melting point ora metal in S-9. In this case, the connection of the case and the lid isperformed in vacuum because the case 158 has no hole to close it invacuum.

In addition, though it is not visible in FIG. 11, the third frequencyadjustment may be performed by laser after the step of the connection ofS-9 to get a small frequency deviation to the nominal frequency when amaterial of the lid is glass. As a result of which it is possible to getthe resonator with the frequency deviation which is within a range of−50 PPM to +50 PPM to the nominal frequency of 10 kHz to 200 kHz, e.g.32.768 kHz. Namely, the nominal frequency, capable of vibrating in afundamental mode is less than 200 kHz. In this step, when the thirdfrequency adjustment is performed, a/an resonance (oscillation)frequency of said resonators is adjusted so that the frequency deviationby the second frequency adjustment is within a range of −950 PPM to +950PPM to the nominal frequency, e.g. 32.768 kHz.

For the step of B, the tuning fork base 145 of the formed resonator 160is first mounted on a mounting portion 159 of a case 165 by conductiveadhesives 161 or solder in S-10, in addition, in S-11 the case 165 and alid 163 are connected by the same way as that of S-9, in more detail,after the resonator was mounted on the mounting portion of the case orafter the resonator was mounted at the mounting portion, and the caseand the lid were connected, the second adjustment of resonance(oscillation) frequency is performed so that a frequency deviation isgenerally within a range of −100 PPM to +100 PPM to a nominal frequencyof 10 kHz to 200 kHz, e.g. 32.768 kHz in vacuum, but, it may be within awider range, for example, −950 PPM to +950 PPM when the third frequencyadjustment as will be shown as follows, is performed. Finally, a hole167 constructed at the case 165 is closed in vacuum using such a metal166 as solder or glass with the low melting point in S-12.

Also, similar to the step of A, the third adjustment of resonance(oscillation) frequency may be performed by laser after the step of S-12to get a small frequency deviation to the nominal frequency. As a resultof which it is possible to get the resonator with the frequencydeviation which is within a range of −50 PPM to +50 PPM to the nominalfrequency, e.g. 32.768 kHz. Thus, a frequency deviation of theresonators in the case of A and B is finally within a range of −100 PPMto +100 PPM at most. Also, the second frequency adjustment may beperformed after the case and the lid were connected and the hole wasclosed in vacuum. In addition, the hole is constructed at the case, butmay be constructed at the lid. Also, the frequency adjustment of thepresent invention is performed in vacuum or inert gas such as nitrogengas or atmosphere, and the values described above are values in vacuum.

Therefore, the flexural mode, quartz crystal tuning fork resonators andthe quartz crystal units manufactured by the above-described method areminiaturized and realized with a small series resistance R₁, a highquality factor Q₁ and low price.

Moreover, in the above-described embodiment, though the first frequencyadjustment of the resonators is performed in the quartz crystal waferand at the same time, when there is a failure resonator, something ismarked on it or it is removed from the quartz crystal wafer, but thepresent invention is not limited to this, namely, the present inventionmay include the step to inspect the flexural mode, quartz crystal tuningfork resonators formed in the quartz crystal wafer therein, in otherwords, the step to inspect whether there is a failure resonator or notin the quartz crystal wafer. When there is a failure resonator in thewafer, something is marked on it or it is removed from the wafer or itis remembered by a computer. By including the step, it can increase theyield because it is possible to find out the failure resonator in anearly step and the failure resonator does not go to the next step. As aresult of which low priced flexural mode, quartz crystal tuning forkresonators can be provided with excellent electrical characteristics.

In this embodiment, the frequency adjustment is performed three times bya separate step, but may be performed at least twice by a separate step.For example, the third frequency adjustment may be omitted. In addition,in order to construct a quartz crystal oscillator, two electrodeterminals of the resonators are connected electrically to an amplifier,capacitors and resistors. In other words, a quartz crystal oscillatingcircuit is constructed and connected electrically so that anamplification circuit comprises a CMOS inverter and a feedback resistorand a feedback circuit comprises a flexural mode, quartz crystal tuningfork resonator, a drain resistor, a capacitor of a gate side and acapacitor of a drain side. Also, the third frequency adjustment may beperformed after the quartz crystal oscillating circuit was constructedin a quartz crystal unit.

Likewise, the flexural mode quartz crystal resonator of a tuning forktype has two tuning fork tines in the present embodiments, butembodiments of the present invention include tuning fork tines more thantwo. In addition, the quartz crystal tuning fork resonators of thepresent embodiments are housed in a package (unit) of a surface mountingtype comprising a case and a lid, but may be housed in a package of atubular type.

In addition, for the tuning fork resonators constructing the quartzcrystal oscillators of the first embodiment to the fourth embodiment ofthe present invention, the resonators are provided so that a capacitanceratio r₁ of a fundamental mode vibration gets smaller than a capacitanceratio r₂ of a second overtone mode vibration, in order to obtain afrequency change of the fundamental mode vibration larger than that ofthe second overtone mode vibration, versus the same change of a value ofload capacitance C_(L). Namely, a variable range of a frequency of thefundamental mode vibration gets wider than that of the second overtonemode vibration.

In more detail, for example, when C_(L)=18 pF and the C_(L) changes in 1pF, the frequency change of the fundamental mode vibration becomeslarger than that of the second overtone mode vibration because thecapacitance ratio r₁ is smaller than the capacitance ratio r₂.Therefore, there is a remarkable effect for the fundamental modevibration, such that the resonators can be provided with the frequencyvariable in the wide range, even when the value of load capacitanceC_(L) changes slightly. Accordingly, when a variation of the samefrequency is required, the number of capacitors which are used in thequartz crystal oscillators decreases because the frequency change versusload capacitance 1 pF becomes large, as compared with that of the secondovertone mode vibration. As a result, the low priced oscillators can beprovided.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

In detail, the tuning fork resonator of this embodiment is provided sothat the influence on resonance frequency of the fundamental modevibration by the shunt capacitance becomes smaller than that of thesecond overtone mode vibration by the shunt capacitance, namely, so thatit satisfies a relationship of S₁=r₁/2Q₁ ²<S₂ =r₂/2Q₂ ², preferably,S₁<S₂/2. As a result, the tuning fork resonator, capable of vibrating inthe fundamental mode and having a high frequency stability can beprovided because the influence on the resonance frequency of thefundamental mode vibration by the shunt capacitance becomes so extremelysmall as it can be ignored. Also, the present invention replaces r₁/2Q₁² with S₁ and r₂/2Q₂ ² with S₂, respectively, and here, S₁ and S₂ arecalled “a stable factor of frequency” of the fundamental mode vibrationand the second overtone mode vibration.

In addition, when a power source is applied to the quartz crystaloscillating circuit, at least one oscillation which satisfies anamplitude condition and a phase condition of vibration starts in thecircuit, and a spent time to get to about ninety percent of the steadyamplitude of the vibration is called “rise time”. Namely, the shorterthe rise time becomes, the easier the oscillation becomes. When risetime t_(r1) of the fundamental mode vibration and rise time t_(r2) ofthe second overtone mode vibration in the circuit are taken, t_(r1) andt_(r2) are given by t_(r1)=kQ₁/(ω₁ (−1+|−RL₁|/R₁)) andt_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁and ω₂ are an angular frequency for the fundamental mode vibration andthe second overtone mode vibration, respectively.

From the above-described relation, it is possible to obtain the risetime t_(r1) of the fundamental mode vibration less than the rise timet_(r2) of the second overtone mode vibration. As an example, whenresonance (oscillation) frequency of a flexural mode, quartz crystaltuning fork resonator is about 32.768 kHz for a fundamental modevibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 andl₁/l=0.48, though there is a distribution in production, as an example,the resonator has a value of Q₁=62,000 and Q₂=192,000, respectively. Inthis embodiment, Q₂ has a value of about three times of Q₁. Accordingly,to obtain the t_(r1) less than the t_(r2), it is necessary to satisfy arelationship of |−RL₁|/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁approximately. Also, according to this invention, the relationship isnot limited to the quartz crystal oscillating circuit comprising theresonator in this embodiment, but this invention also includes allquartz crystal oscillating circuits to satisfy the relationship. Byconstructing the oscillating circuit like this, a quartz crystaloscillator with the flexural mode, quartz crystal tuning fork resonatorcan be provided with a short rise time. In other words, an output signalof the oscillator has an oscillation frequency of the fundamental modevibration of the resonator and is outputted through a buffer circuit.Namely, the second overtone mode vibration can be suppressed in theoscillating circuit. In this embodiment, the resonator has also a valueof r₁=320 and r₂=10,600 as an example. According to this invention, r₁has a value of 210 to 520.

The above-described quartz crystal resonators are formed by at least onemethod of chemical, mechanical and physical methods. The mechanicalmethod, for example, uses a particle such as GC#1000 and the physicalmethod, for example, uses atom or molecule. Therefore, these methods arecalled “a particle method” here.

Thus, the electronic apparatus of this invention comprising a displayportion and a quartz crystal oscillator at least may operate normallybecause the quartz crystal oscillator comprises the quartz crystaloscillating circuit with a high frequency stability, namely, a highfrequency reliability.

As described above, it will be easily understood that the electronicapparatus comprising the quartz crystal oscillator comprising the quartzcrystal oscillating circuit having the flexural mode, quartz crystaltuning fork resonator with novel shapes, the novel electrodeconstruction and excellent electrical characteristics, according to thepresent invention, may have the outstanding effects. Similar to this, itwill be easily understood that the electronic apparatus comprising thequartz crystal oscillator comprising the quartz crystal oscillatingcircuit having the length-extensional mode quartz crystal resonator withthe novel cutting angle and the novel shape, according to the presentinvention, may have also the outstanding effect. In addition to this,while the present invention has been shown and described with referenceto preferred embodiments thereof, it will be understood by those skilledin the art that the changes in shape and electrode construction can bemade therein without departing from the spirit and scope of the presentinvention.

1. A quartz crystal resonator capable of vibrating in a flexural mode ofan inverse phase, the quartz crystal resonator comprising: a quartzcrystal tuning fork base; first and second quartz crystal tuning forktines connected to the quartz crystal tuning fork base, each of thefirst and second quartz crystal tuning fork tines having a first mainsurface and a second main surface opposite the first main surface and agroove having a plurality of stepped portions formed in at least one ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines; and an electrode disposed in thegroove formed in at least one of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that amerit value M₁ of a fundamental mode of vibration of the quartz crystaltuning fork resonator is greater than a merit value M₂ of a secondovertone mode of vibration thereof, the merit values M₁ and M₂ beingdefined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂represent a quality factor of the fundamental mode of vibration and thesecond overtone mode of vibration, respectively, of the quartz crystaltuning fork resonator and r₁ and r₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; wherein apiezoelectric constant e₁₂ of the quartz crystal tuning fork resonatoris within a range of 0.095 C/m² to 0.19 C/m² in the absolute value.
 2. Aquartz crystal resonator according to claim 1; wherein a groove having aplurality of stepped portions is formed on each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; and wherein an electrode is disposed in each of the groovesformed on each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a merit valueM₁ of the fundamental mode of vibration of the quartz crystal tuningfork resonator is greater than 65 and a merit value M₂ of the secondovertone mode of vibration of the quartz crystal tuning fork resonatoris less than
 30. 3. A quartz crystal resonator according to claim 1;wherein the groove formed on at least one of opposite main surfaces ofeach of the quartz crystal tuning fork tines comprises a throughhole. 4.A quartz crystal unit comprising: a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode of an inverse phase, the quartzcrystal tuning fork resonator comprising a quartz crystal tuning forkbase, first and second quartz crystal tuning fork tines connected to thequartz crystal tuning fork base and each having a first main surface anda second main surface opposite the first main surface, a groove having aplurality of stepped portions formed in at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines, and an electrode disposed in the groove formed in atleast one of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a merit value M₁ of afundamental mode of vibration of the quartz crystal tuning forkresonator is greater than a merit value M₂ of a second overtone mode ofvibration thereof, the merit values M₁ and M₂ being defined by theratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent aquality factor of the fundamental mode of vibration and the secondovertone mode of vibration, respectively, of the quartz crystal tuningfork resonator and r₁ and r₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; a case forhousing the quartz crystal tuning fork resonator; and a lid for coveringan open end of the case; wherein a piezoelectric constant e₁₂ of thequartz crystal tuning fork resonator is within a range of 0.095 C/m² to0.19 C/m² in the absolute value.
 5. A quartz crystal unit according toclaim 4; wherein a groove having a plurality of stepped portions isformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a width of atleast one of the grooves formed in the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines is withina range of 0.03 mm to 0.12 mm; wherein a spaced-apart distance betweenthe first and second quartz crystal tuning fork tines is within a rangeof 0.05 mm to 0.35 mm and greater than or equal to the width of at leastone of the grooves; and wherein a length of at least one of the groovesformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines is within a range of 40% to 80%of a length of each of the first and second quartz crystal tuning forktines.
 6. A quartz crystal unit according to claim 4; wherein a groovehaving a plurality of stepped portions is formed in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines; and wherein an electrode is disposed in the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a capacitanceratio r₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than a capacitance ratio r₂ of the secondovertone mode of vibration thereof.
 7. A quartz crystal unit accordingto claim 4; wherein a groove having a plurality of stepped portions isformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a width W₂ ofat least one of the grooves formed in the first and second main surfacesof each of the first and second quartz crystal tuning fork tines iswithin a range of 0.03 mm to 0.12 mm; wherein the groove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines has an inner stepped portion and anouter stepped portion opposite to the inner stepped portion in the widthdirection of the corresponding one of the first and second quartzcrystal tuning fork tines; wherein each of the first and second quartzcrystal tuning fork tines has side surfaces comprising an inner sidesurface and an outer side surface opposite to the inner side surface,the inner stepped portion being opposite to the inner side surface, andthe outer stepped portion being opposite to the outer side surface; andfurther comprising a first electrode disposed on each of the inner andouter stepped portions of the groove formed in each of the first andsecond main surfaces of the first and second quartz crystal tuning forktines and a second electrode disposed on each of the inner and outerside surfaces of the first and second quartz crystal tuning fork tines;wherein the first electrodes disposed on the inner and outer steppedportions of the grooves of the first quartz crystal tuning fork tine areconnected to the second electrodes disposed on the inner and outer sidesurfaces of the second quartz crystal tuning fork tine so that the firstelectrodes of the first quartz crystal tuning fork tine and the secondelectrodes of the second quartz crystal tuning fork tine define a firstelectrode terminal; and wherein the second electrodes disposed on theinner and outer side surfaces of the first quartz crystal tuning forktine are connected to the first electrodes disposed on the inner andouter stepped portions of the grooves of the second quartz crystaltuning fork tine so that the second electrodes of the first quartzcrystal tuning fork tine and the first electrodes of the second quartzcrystal tuning fork tine define a second electrode terminal.
 8. A quartzcrystal unit according to claim 4; wherein a spaced-apart distancebetween the first and second quartz crystal tuning fork tines is withina range of 0.05 mm to 0.35 mm; wherein a groove having a plurality ofstepped portions is formed in each of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines so thatthe spaced-apart distance between the first and second quartz crystaltuning fork tines is greater than or equal to a width of at least one ofthe grooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines; wherein the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines has a base portion;and wherein an electrode is disposed on the base portion of the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that the electrodesdisposed on the base portions of the grooves of the first quartz crystaltuning fork tine have an electrical polarity opposite to an electricalpolarity of the electrodes disposed on the base portions of the groovesof the second quartz crystal tuning fork tine.
 9. A quartz crystal unitaccording to claim 4; wherein a groove having a plurality of steppedportions is formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines; wherein thequartz crystal tuning fork base has a cut portion; and wherein a lengthof the quartz crystal tuning fork base is less than 0.5 mm.
 10. A quartzcrystal unit according to claim 4; wherein a groove having a pluralityof stepped portions is formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines; wherein stable factors S₁ and S₂ of the fundamental mode ofvibration and the second overtone mode of vibration of the quartzcrystal tuning fork resonator are defined by S₁=r₁/2Q₁ ² and S₂=r₂/2Q₂², respectively; and wherein an electrode is disposed on the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that S₁ is lessthan S₂.
 11. A quartz crystal unit according to claim 4; wherein thequartz crystal tuning fork base has a cut portion; and wherein thequartz crystal tuning fork resonator has a frame portion protruding fromthe quartz crystal tuning fork base and mounted on a mounting portion ofthe case.
 12. A quartz crystal oscillator comprising: a quartz crystaloscillating circuit comprised of an amplification circuit comprising aCMOS inverter and a feedback resistor, and a feedback circuit comprisinga quartz crystal tuning fork resonator capable of vibrating in aflexural mode of an inverse phase, a plurality of capacitors and a drainresistor, the quartz crystal tuning fork resonator comprising a quartzcrystal tuning fork base, first and second quartz crystal tuning forktines connected to the quartz crystal tuning fork base and each having afirst main surface and a second main surface opposite the first mainsurface, a groove having a plurality of stepped portions formed in atleast one of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines, and an electrode being disposedin the groove formed in at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that a merit value M₁ of a fundamental mode of vibration of thequartz crystal tuning fork resonator is greater than a merit value M₂ ofa second overtone mode of vibration thereof, the merit values M₁ and M₂being defined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ andQ₂ represent a quality factor of the fundamental mode of vibration andthe second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator and r₁ and r₂ represent a capacitanceratio of the fundamental mode of vibration and the second overtone modeof vibration, respectively, of the quartz crystal tuning fork resonator;wherein a piezoelectric constant e₁₂ of the quartz crystal tuning forkresonator is within a range of 0.095 C/m² to 0.19 C/m² in the absolutevalue.
 13. A quartz crystal oscillator according to claim 12; wherein aratio of an amplification rate α₁ of the fundamental mode of vibrationand an amplification rate α₂ of the second overtone mode of vibration ofthe amplification circuit is greater than that of a feedback rate β₂ ofthe second overtone mode of vibration and a feedback rate β₁ of thefundamental mode of vibration of the feedback circuit, and a product ofthe amplification rate α₁ and the feedback rate β₁ of the fundamentalmode of vibration is greater than 1; wherein a groove having a pluralityof stepped portions is formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines; and wherein an electrode is disposed in the groove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a series resistance R₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than a series resistance R₂ of the second overtonemode of vibration thereof.
 14. A quartz crystal oscillator according toclaim 12: wherein a ratio of an absolute value of negative resistance−RL₁ of the fundamental mode of vibration of the amplification circuitand a series resistance R₁ of the fundamental mode of vibration of thequartz crystal tuning fork resonator is greater than that of an absolutevalue of negative resistance −RL₂ of the second overtone mode ofvibration of the amplification circuit and a series resistance R₂ of thesecond overtone mode of vibration thereof; wherein a qroove having aplurality of stepped portions is formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; and wherein an electrode is disposed in the qroove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a capacitance ratio r₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than a capacitance ratio r₂ of the second overtonemode of vibration thereof.
 15. A quartz crystal oscillator according toclaim 12; wherein |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where |−RL₁|and |−RL₂| represent an absolute value of negative resistance of thefundamental mode of vibration and the second mode of vibration of theamplification circuit, and R₁ and R₂ represent a series resistance ofthe fundamental mode of vibration and the second overtone mode ofvibration of the quartz crystal tuning fork resonator.
 16. A quartzcrystal oscillator according to claim 12: wherein a groove having aplurality of stepped portions is formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; wherein an electrode is disposed in the groove formed in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a capacitance ratio r₁ of thefundamental mode of vibration of the quartz crystal tuning forkresonator is less than a capacitance ratio r₂ of the second overtonemode of vibration thereof; and wherein the quartz crystal oscillatingcircuit outputs through a buffer circuit an output signal an oscillationfreguency of about 32.768 kHz with a freguency deviation within therange of −100 PPM to +100 PPM.
 17. A quartz crystal oscillator accordingto claim 12; wherein at least one qroove having a plurality of steppedportions is formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines so that a ratioW₂/W is greater than 0.35 and less than 1, where W₂ represents a widthof at least one of the grooves formed in the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines and W represents a width of each of the quartz crystal tuning forktines; and wherein a length of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 40% to 80% of a length ofeach of the first and second quartz crystal tuning fork tines.
 18. In anelectronic apparatus having a display portion: at least one quartzcrystal oscillator comprising a quartz crystal oscillating circuitcomprised of an amplification circuit having at least an amplifier, anda feedback circuit comprising at least a quartz crystal tuning forkresonator capable of vibrating in a flexural mode of an inverse phase,the quartz crystal tuning fork resonator comprising a quartz crystaltuning fork base, first and second quartz crystal tuning fork tinesconnected to the quartz crystal tuning fork base and each having a firstmain surface and a second main surface opposite the first main surface,a groove having a plurality of stepped portions formed in at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines, and an electrode disposed in thegroove formed in at least one of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that amerit value M₁ of a fundamental mode of vibration of the quartz crystaltuning fork resonator is greater than a merit value M₂ of a secondovertone mode of vibration thereof, the merit values M₁ and M₂ beingdefined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂represent a quality factor of the fundamental mode of vibration and thesecond overtone mode of vibration, respectively, of the quartz crystaltuning fork resonator and r₁ and r₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; wherein apiezoelectric constant e₁₂ of the quartz crystal tuning fork resonatoris within a range of 0.095 C/m² to 0.19 C/m² in the absolute value. 19.An electronic apparatus according to claim 18; wherein at least onegroove having a plurality of stepped portions is formed in each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines; wherein each of the fundamental mode ofvibration and the second overtone mode of vibration of the quartzcrystal tuning fork resonator is driven by the piezoelectric constante₁₂ within the range of 0.095 C/m² to 0.19 C/m² in the absolute value;wherein |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where |−RL₁| and |−RL₂|represent an absolute value of negative resistance of the fundamentalmode of vibration and the second overtone mode of vibration of theamplification circuit, and R₁ and R₂ represent a series resistance ofthe fundamental mode of vibration and the second overtone mode ofvibration of the quartz crystal tuning fork resonator; and wherein anoutput signal of the quartz crystal oscillating circuit is a clocksignal for use in operation of the electronic apparatus to display timeinformation at the display portion, the clock signal having anoscillation freguency of the fundamental mode of vibration.
 20. Anelectronic apparatus according to claim 19; wherein the amplificationcircuit of the quartz crystal oscillating circuit has a CMOS inverterand a feedback circuit, the feedback circuit having the quartz crystaltuning fork resonator, a plurality of capacitors and a drain resistor,the quartz crystal tuning fork resonator being electrically connected tothe amplification circuit and to the plurality of capacitors and thedrain resistor of the feedback circuit; wherein the at least one quartzcrystal oscillator comprises a quartz crystal oscillating circuitcomprisinq a quartz crystal resonator, an amplifier, a plurality ofresistors, and a plurality of capacitors, a mode of vibration of thequartz crystal resonator of the quartz crystal oscillating circuitbeincr different from that of the quartz crystal tuning fork resonator;and wherein the quartz crystal resonator of the quartz crystaloscillating circuits comprises a quartz crystal one of alength-extensional mode quartz crystal resonator, a thickness shear modequartz crystal resonator, a width-extensional mode quartz crystalresonator, a Lame mode quartz crystal resonator and a SAW resonator. 21.An electronic apparatus according to claim 18; wherein the at least onequartz crystal oscillator comprises a quartz crystal oscillating circuitcomprised of an amplification circuit having an amplifier and a feedbackresistor, and a feedback circuit comprising a quartz crystal resonator,a plurality of capacitors and a drain resistor, the quartz crystalresonator being a length-extensional mode quartz crystal resonatorcomprised of a vibrational portion having a length greater than a widthand a thickness smaller than the width, connecting portions located atends of the vibrational portion, supporting portions connected to thevibrational portion through the connecting portions, and electrodesdisposed opposite each other on upper and lower faces of the vibrationalportion; wherein a piezoelectric constant e₁₂ of the length-extensionalmode resonator is within a range of 0.095 C/m² to 0.19 C/m² in theabsolute value; and wherein the quartz crystal oscillating circuitoutputs a signal through a buffer circuit, the output signal being aclock signal for use in operation of the electronic apparatus.
 22. Anelectronic apparatus according to claim 18; wherein at least one groovehaving a plurality of stepped portions is formed in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines; wherein each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines has acentral linear portion; wherein the at least one groove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is greater than adistance in the width direction of the at least one groove measured froman outer edge of the at least one groove to an outer edge of thecorresponding one of the first and second quartz crystal tuning forktines; wherein a length of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 40% to 80% of a length ofeach of the first and second quartz crystal tuning fork tines; andwherein an output signal of the quartz crystal oscillating circuit is aclock signal for use in operation of the electronic apparatus to displaytime information at the display portion, the clock signal having anoscillation frequency of the fundamental mode of vibration.
 23. A methodfor manufacturing an electronic apparatus, comprising the steps of:providing a display portion; forming at least one quartz crystal tuningfork resonator capable of vibrating in a flexural mode of an inversephase and having a fundamental mode of vibration, a second overtone modeof vibration, a quartz crystal tuning fork base, and first and secondquartz crystal tuning fork tines connected to the quartz crystal tuningfork base and each having side surfaces; disposing an electrode on eachof two of the side surfaces of each of the first and second quartzcrystal tuning fork tines so that the electrodes disposed on the sidesurfaces of the first quartz crystal tuning fork tine have an electricalpolarity opposite to an electrical polarity of the electrodes disposedon the side surfaces of the second quartz crystal tuning fork tine;providing at least one quartz crystal oscillator comprising a quartzcrystal oscillating circuit comprised of an amplification circuit havinga CMOS inverter and a feedback resistor, and a feedback circuit havingthe quartz crystal tuning fork resonator; mounting the quartz crystaltuning fork resonator on a mounting portion of a case using a conductiveadhesive or solder; and adjusting an oscillation frequency of the quartzcrystal tuning fork resonator so that the quartz crystal oscillatingcircuit outputs an output signal of the oscillation frequency of about32.768 kHz with a frequency deviation within a range of −100 PPM to +100PPM; wherein a ratio of an absolute value of negative resistance −RL₁ ofthe fundamental mode of vibration of the amplification circuit and aseries resistance R₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is greater than a ratio of an absolutevalue of negative resistance −RL₂ of the second overtone mode ofvibration of the amplification circuit and a series resistance R₂ of thesecond overtone mode of vibration thereof; wherein a merit value M₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than a merit value M₂ of the second overtone modeof vibration thereof, the merit values M₁ and M₂ being defined by theratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent aquality factor of the fundamental mode of vibration and the secondovertone mode of vibration, respectively, of the quartz crystal tuningfork resonator and r₁ and r₂ represent a capacitance ratio of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator; and wherein apiezoelectric constant e₁₂ of the quartz crystal tuning fork resonatoris within a range of 0.095 C/m² to 0.19 C/m² in the absolute value. 24.A method according to claim 23; further comprising the step ofelectrically connecting the quartz crystal tuning fork resonator to theamplification circuit; and wherein an output signal of the quartzcrystal oscillating circuit comprises a clock signal for use inoperation of the electronic apparatus to display time information at thedisplay portion, the clock signal having an oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator.
 25. A method according to claim 24; wherein the quartzcrystal oscillating circuit comprises a quartz crystal resonator, anamplifier, a plurality of resistors, and a plurality of capacitors, thequartz crystal resonator comprising one of a length-extensional modequartz crystal resonator, a thickness shear mode quartz crystalresonator, a width-extensional mode quartz crystal resonator, a Lamemode quartz crystal resonator, and a SAW resonator; wherein a mode ofvibration of the quartz crystal resonator is different from that of thequartz crystal tuning fork resonator capable of vibrating in a flexuralmode; and wherein an output signal of the quartz crystal oscillatingcircuit comprises a clock signal for use in operation of the electronicapparatus.
 26. A method according to claim 23; wherein the forming stepincludes the steps of forming a plurality of the quartz crystal tuningfork resonators in a quartz crystal wafer, inspecting the quartz crystalwafer to identify any damaged quartz crystal tuning fork resonators, andeither marking the damaged quartz crystal tuning fork resonators in thequartz crystal wafer, storing in a computer identification informationcorresponding to the damaged quartz crystal tuning fork resonators, orremoving from the quartz crystal wafer the damaged quartz crystal tuningfork resonators.
 27. A method according to claim 23; wherein each of thefirst and second quartz crystal tuning fork tines has first and secondopposite main surfaces and first and second opposite side surfaces;wherein the forming step further comprises the step of forming a groovehaving a plurality of stepped portions in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; wherein the disposing step comprises the steps of disposing afirst electrode on each of at least two of the stepped portions of thegroove in each of the first and second main surfaces of the first andsecond quartz crystal tuning fork tines and a second electrode on eachof the first and second side surfaces of each of the first and secondquartz crystal tuning fork tines; and wherein an output signal of thequartz crystal oscillating circuit comprises a clock signal for use inoperation of the electronic apparatus to display time information at thedisplay portion, the clock signal having an oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator.
 28. A method according to claim 27; wherein the forming stepcomprises the steps of forming the first and second quartz crystaltuning fork tines in a first etching process; and forming at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines in a secondetching process different from the first etching process, the step offorming the first and second quartz crystal tuning fork tines beingperformed before the step of forming the at least one of the groovesformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines; and further comprising thesteps of connecting the first electrodes disposed on at least two of thestepped portions of the groove formed in each of the first and secondmain surfaces of the first quartz crystal tuning fork tine to the secondelectrodes disposed on the first and second side surfaces of the secondquartz crystal tuning fork tine to form a first electrode terminal, andconnecting the second electrodes disposed on the first and second sidesurfaces of the first quartz crystal tuning fork tine to the firstelectrodes disposed on at least two of the stepped portions of thegroove formed in each of the first and second main surfaces of thesecond quartz crystal tuning fork tine to form a second electrodeterminal.
 29. A method according to claim 28; further comprising thestep of electrically connecting the quartz crystal tuning fork resonatorto the amplification circuit and to the capacitors and the drainresistor of the feedback circuit; wherein the at least one quartzcrystal oscillator comprises a quartz crystal oscillating circuitcomprising a quartz crystal resonator, an amplifier, a plurality ofresistors, and a plurality of capacitors, the quartz crystal resonatorcomprising one of a length extensional mode quartz crystal resonator, athickness shear mode quartz crystal resonator, a width extensional modequartz crystal resonator, a Lame mode quartz crystal resonator and a SAWresonator, and a mode of vibration of the quartz crystal resonator ofthe quartz crystal oscillating circuit being different from that of thequartz crystal tuning fork resonator; and wherein an output signal ofthe quartz crystal oscillating circuit comprises a clock signal for usein operation of the electronic apparatus.
 30. A method according toclaim 27; wherein the quartz crystal tuning fork base has a cut portion;wherein the forming step comprises the steps of forming the first andsecond quartz crystal tuning fork tines and the quartz crystal tuningfork base having the cut portion in a first etching process; and formingat least one of the grooves formed in the first and second main surfacesof each of the first and second quartz crystal tuning fork tines in asecond etching process different from the first etching process; andfurther comprising the steps of connecting the first electrodes disposedon at least two of the stepped portions of the groove formed in each ofthe first and second main surfaces of the first quartz crystal tuningfork tine to the second electrodes disposed on the first and second sidesurfaces of the second quartz crystal tuning fork tine to form a firstelectrode terminal; and connecting the second electrodes disposed on thefirst and second side surfaces of the first quartz crystal tuning forktine to the first electrodes disposed on at least two of the steppedportions of the groove formed in each of the first and second mainsurfaces of the second quartz crystal tuning fork tine to form a secondelectrode terminal.
 31. A method according to claim 27; wherein theforming step comprises the steps of forming the first and second quartzcrystal tuning fork tines in a first etching process; and forming atleast one of the grooves formed in the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines in asecond etching process different from the first etching process, thestep of forming the first and second quartz crystal tuning fork tinesbeing performed after the step of forming the at least one of thegrooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines; and furthercomprising the steps of connecting the first electrodes disposed on atleast two of the stepped portions of the groove formed in each of thefirst and second main surfaces of the first quartz crystal tuning forktine to the second electrodes disposed on the first and second sidesurfaces of the second quartz crystal tuning fork tine to form a firstelectrode terminal, and connecting the second electrodes disposed on thefirst and second side surfaces of the first quartz crystal tuning forktine to the first electrodes disposed on at least two of the steppedportions of the groove formed in each of the first and second mainsurfaces of the second quartz crystal tuning fork tine to form a secondelectrode terminal.
 32. A method according to claim 27; wherein theforming step comprises the steps of forming the first and second quartzcrystal tuning fork tines in a first etching process so that aspaced-apart distance between the first and second quartz crystal tuningfork tines is within a range of 0.05 mm to 0.35 mm; and forming at leastone of the grooves formed in the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines in a secondetching process different from the first etching process so that a widthW2 of at least one of the grooves formed in the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is within a range of 0.03 mm to 0.12 mm and a ratio W₂/W isgreater than 0.35 and less than 1, where W represents a width of each ofthe quartz crystal tuning fork tines, the spaced-apart distance betweenthe first and second quartz crystal tuning fork tines being greater thanor equal to the width W₂ of the at least one groove, and the step offorming the first and second quartz crystal tuning fork tines beingperformed before the step of forming the at least one of the groovesformed in the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines.
 33. A method according to claim27; wherein the forming step comprises the steps of forming the firstand second quartz crystal tuning fork tines in a first etching processso that a spaced-apart distance between the first and second quartzcrystal tuning fork tines is within a range of 0.05 mm to 0.35 mm; andforming at least one of the grooves formed in the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines in a second etching process different from the first etchingprocess so that a width W₂ of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 0.03 mm to 0.12 mm and aratio W₂/W is greater than 0.35 and less than 1, where W represents awidth of each of the quartz crystal tuning fork tines, the spaced-apartdistance between the first and second quartz crystal tuning fork tinesbeing greater than or equal to the width W₂ of the at least one groove,and the step of forming the first and second quartz crystal tuning forktines being performed after the step of forming the at least one of thegrooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines.
 34. A methodaccording to claim 27; wherein each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines has a central linear portion; wherein the groove formed in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of at least oneof the grooves formed in the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is greater than adistance in the width direction of the at least one groove measured froman outer edge of the at least one groove to an outer edge of thecorresponding one of the first and second quartz crystal tuning forktines; wherein the forming step comprises the steps of forming the firstand second quartz crystal tuning fork tines in a first etching process,and forming at least one of the grooves formed in the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines in a second etching process, the step of forming the first andsecond quartz crystal tuning fork tines being performed simultaneouslywith the step of forming the at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines; and further comprising the steps ofconnecting the first electrodes disposed on at least two of the steppedportions of the groove formed in each of the first and second mainsurfaces of the first quartz crystal tuning fork tine to the secondelectrodes disposed on the first and second side surfaces of the secondquartz crystal tuning fork tine to form a first electrode terminal, andconnecting the second electrodes disposed on the first and second sidesurfaces of the first quartz crystal tuning fork tine to the firstelectrodes disposed on at least two of the stepped portions of thegroove formed in each of the first and second main surfaces of thesecond quartz crystal tuning fork tine to form a second electrodeterminal.
 35. A method according to claim 27; wherein the forming stepcomprises the steps of forming the first and second quartz crystaltuning fork tines in a first etching process so that a spaced-apartdistance between the first and second quartz crystal tuning fork tinesis within a range of 0.05 mm to 0.35 mm, and forming at least one of thegrooves formed in the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines in a second etchingprocess so that a width W₂ of at least one of the grooves formed in thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 0.03 mm to 0.12 mm and aratio W₂/W is greater than 0.35 and less than 1, where W represents awidth of each of the quartz crystal tuning fork tines, the spaced-apartdistance between the first and second quartz crystal tuning fork tinesbeing greater than or equal to the width W₂ of the at least one groove,and the step of forming the first and second quartz crystal tuning forktines being performed simultaneously with the step of forming the atleast one of the grooves formed in the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines.